In a trapezoid, the smaller base is 3 more than the height, the larger base is 5 less than 3 times the height, and the area is 45 square centimeters. Find the height in centimeters. Use an algebraic solution.

The area of a trapezoid is the average of the bases times the height ...

A=h (b1+b2) / 2

2A=h (b1+b2)

h = (2A) / (b1+b2)

b1=h+3, b2=3h-5, A=45 so

h = (2*45) / (h+3+3h-5)

h=90 / (4h-2)

4h^2-2h=90

4h^2-2h-90=0

2 (2h^2-h-45) = 0

2 (2h^2-10h+9h-45) = 0

2 (2h (h-5) + 9 (h-5) = 0

2 (2h+9) (h-5) = 0 since h>0

h=5 cm

The height would be 5cm